Massively Parallel Curved Spectral/Finite Element Mesh Generation of Industrial CAD Geometries in Two and Three Dimensions

A scalable paradigm is developed to generate 2D/3D high quality finite/spectral element meshes containing arbitrarily curved elements. The current methodology begins with a linear mesh that is decomposed using a graph partitioning scheme. Higher-order elements are then created from the linear mesh, where a CAD model must be queried in order for the curved faces/edges to conform to the boundaries. Subsequently, the curved elements are directly generated using analytical maps which transform the point distribution of the master element to the element in physical space. These analytic maps are derived for triangular, quadrilateral, tetrahedral, prismatic, pyramidal, and hexahedral elements. It is shown that the stretching of Chebyshev/Fekete point distributions are also preserved by these maps and hence they can be used to generate well-conditioned spectral element grids. Since these maps require a computationally intensive min-distance projection to the CAD model, a fast min-distance search algorithm is proposed. The current method is embarrassingly parallel, uses MPI, and is implemented on a commodity cluster. Degradation in performance is observed with load balancing based on maximizing the volume to surface ratio and, therefore, a new load balancing is proposed to mitigate this loss in speed-up. Results are presented for a two-dimensional cylinder, NACA0012 airfoil, 30P30N high-lift geometry, a three-dimensional sphere, a notional missile configuration and a civil aircraft geometry.